This paper analyzes an effective technique for stabilizing pure explicit time dif­ ferencing in the numerical computation of multidimensional nonlinear parabolic equations. The method uses easily synthesized linear smoothing operators at each time step to quench the instabil­ ity. Smoothing operators based on positive real powers of the negative Laplacian are helpful, and (−Δ)p can be realized ...

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...

We consider solutions to the incompressible Navier–Stokes equations on the periodic domain Ω = [0, 2π] with potential body forces. Let R ⊆ H(Ω) denote the set of all initial data that lead to regular solutions. Our main result is to construct a suitable Banach space S A such that the normalization map W : R → S A is continuous, and such that the normal form of the Navier–Stokes equations is a w...

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

in this paper, the ultraspherical operational matrices of derivatives are constructed. based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear lane-emden type singular initial value problems. the basic idea behind the suggested algorithms is basically built on transforming the eq...

The general class of problems we consider is the following: Let Ω1 be a bounded domain in R d for d ≥ 2 and let u be a velocity field on all of R. Suppose that for all R ≥ 1 we have an operator TR that projects u restricted to RΩ1 (Ω1 scaled by R) into a function space on RΩ1 for which the solution to some initial value problem is well-posed with TRu 0 as the initial velocity. Can we show that ...

In this paper, we study the global well-posedness of the 2D compressible NavierStokes equations with large initial data and vacuum. It is proved that if the shear viscosity μ is a positive constant and the bulk viscosity λ is the power function of the density, that is, λ(ρ) = ρβ with β > 3, then the 2D compressible Navier-Stokes equations with the periodic boundary conditions on the torus T2 ad...

In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...

The weak sequential compactness of reflexive Banach spaces is used to explain the fact that certain ill-posed, linear problems become well-posed if the solutions are required to satisfy a prescribed bound. Applications are made to the computability of solutions of ill-posed problems associated with elliptic and parabolic partial differential equations.

Developing theory, algorithms, and software tools for analyzing matrix pencils whose matrices have various structures are contemporary research problems. Such matrices are often coming from discretizations of systems of differential-algebraic equations. Therefore preserving the structures in the simulations as well as during the analyses of the mathematical models typically means respecting the...